" sec?x х dx tan"x 5. ,

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 31E
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Trigonometric integrals Evaluate the following integrals.

"
sec?x
х
dx
tan"x
5.
,
Transcribed Image Text:" sec?x х dx tan"x 5. ,
Expert Solution
Step 1

Evaluate,

sec2xtan5xdx

Step 2

Simplification:

We have

sec2xtan5xdx        ...(1)

Substitute tanx=usec2xdx=du in (1),

sec2xtan5xdx=1u5du=u-5du=u-5+1-5+1+C=u-4-4+C=-14u4+C=-14tan4x+C             Since u=tanx

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